The theory behind the glide path is easily distilled: as we grow older and approach retirement, we transition from an primary objective of growth to one of capital preservation. Our allocation profile, therefore, should follow this transition.

Close to retirement, when capital preservation is paramount, stocks are riskier than bonds. Further from retirement, when growth is more critical, bonds are actually riskier than stocks.

As glide paths go, that's where the agreements end and the disagreements begin.

For a simple concept, glide paths are a complicated beast. We have to consider things such as:

**To versus through**: Do we assume the investor is going to hold this portfolio*to*the date of retirement or*through*their retirement?**Risk preference assumptions**: All investors do not share the same risk preferences, but when we ascribe a global glide path, we assume they do.*How*those risk preferences are modeled, however, can have a huge impact on the shape of the curve.**Asset class constraints:**Glide paths are often the delineating line between stocks and bonds – but what about alternatives? What about high carry hybrids? If, how, and what category these asset classes get lumped into can dramatically change the shape of the curve.**Income growth rates & savings rates:**Investors tend to both earn more, on constant-dollar basis, as well as save more, later in life.**Asset class growth rates:**The expected return, volatility, and correlation profiles of the asset classes that get put into the process can dramatically skew the resulting curve.

Betterment's method for constructing their glide path was recently shared with me and they use one of the more unique methods I've seen for coming up with their final curve.

First, Betterment finds, at each point in time, the asset allocation mix that provide the best returns for a given percentile.

We can think of it like this: for each year in the glide path, we run a whole mess of simulations giving us stock and bond returns up to that point. So let's say we do 10,000 simulations. We then translate these returns into returns for portfolios with different stock/bond mixes. This gives us 10,000 portfolio returns for each asset allocation profile.

Given the percentile we're examining – let's say its the 15th – we would find the 15th percentile return for each asset allocation profile. The simple way of doing this is sort the 10,000 returns from worst to best and selecting the 150th one.

We would then take the asset allocation profile that has the *best *return, given that we are looking at 15th percentile returns. This would be the allocation profile we select given that year in the curve and the percentile we are targeting.

Betterment plots out how some of these curves play out given the years and selected percentiles.

We can see that the results of each curve are fairly easy to interpret. For really, really bad cases of returns (5th percentile), we end up in bonds for almost the entire curve. For better cases (50th percentile), we end up transitioning entirely to stocks very early on.

Betterment then averages all these curves together to get their final glide path.

Now, before I go any further, I want to applaud Betterment's transparency and the ingenuity of their process. The rest of this post is not meant as an indictment of their process: I just wanted to utilize someone else's established process to explore the implications of what happens when we change our assumptions.

And the biggest assumption I wanted to explore was this: what if the future doesn't look like the past?

To be clear, I'm not saying Betterment made this assumption - I just want to show the problems if you tried to apply Betterments process with bad assumptions.

Now, theoretically, that's what simulation is supposed to do in the first place: give us a view of the world as it *could *have been. Most of the time, we use some sort of Monte Carlo process, sampling from actual historical returns to create an alternate reality.

The problem is, however, is that our results are ultimately limited by the results of the past. Even if we look at 50-100 year horizons, we're still potentially introducing biases based on what happened over those years. Does it really make sense to keep sampling from U.S. stock returns in a period during which we ascended to world economic superpower? I mean, you can pull that trick off once...

In the finance industry, we plaster "past performance is not indicative of future results" on every piece of marketing material we touch. So why is it we assume past performance is indicative of future results when it comes to performance simulations?

What if our past was really that of Japan? I expect that our attitude towards – and appetite for – equities would be quite different.

To explore this idea of truly alternate realities, I wanted to use Betterment's glide path construction methodology, but step outside the U.S.-based statistics. So I downloaded local currency stock returns from MSCI for a whole bunch of different countries, from 1970-2015, and ran the process. The results are staggering:

Now, it should be noted that I assumed a constant 3% return for fixed-income for *all *countries. Clearly this isn't an accurate assumption, but I wanted to focus this analysis particularly on equities, which meant holding everything else equal.

With the most aggressive glide path is Sweden, who over the period had a compound annual growth rate ("CAGR") of 11.23% and an annualized volatility of 21.90%. You can see that with this aggressive annualized return profile, the suggestion is to hold a very significant amount of equities over the entire glide path.

The United States is right up there in 2nd place, with one of the highest annualized growth rates and one of the lowest volatility profiles.

At the bottom is Austria, who returned a paltry CAGR of 3.48% with a volatility of 20.83%. Given that stocks returned only 0.48% more than our bonds, with significantly more volatility (as our bond return had 0% volatility), the suggestion is to hold little in the way of stocks.

It seems like as far as alternate realities go, the history of U.S. returns is on the rosier side of things – hence our fairly aggressive glide paths.

Before we put our dollars to work, it is always important to understand the assumptions that underpin our allocations. In the case of glide paths, it seems common to assume that, on average and over the long run, past returns will indeed be indicative of future results.

But when our past is comprised of the 90th percentile of global stock returns and the the 5th percentile of global stock volatility, we have to wonder: are we working from a realistic base of assumptions?

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